Geodesic
Algebras of observables of the free Dirac field
Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 2, pp. 166-182 Cet article a éte moissonné depuis la source Math-Net.Ru

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A net of algebras of local observables of the free Dirac field satisfying the Haag–Araki axioms is constructed and investigated. It is shown that because of the $C$-number nature of the commutation relations the model also satisfies the axiom of weak additivity, in contrast to fermion systems of general form. A new representation for a spinor field is constructed that is unitarily equivalent to the usual one and taken as a basis for constructing a net of algebras of observables of threedimensional regions on the $t=0$ hyperplane of Minkowski space. It is shown that the algebra of observables of a three-dimensional region $B$ coincides with that of the four-dimensional double cone $C(B)$ with base $B$. This correspondence is used to prove structure theorems for the algebras of observables of the regions $C(B)$ and $C(B)'$. The methods of Tomita–Takesaki theory are used to show that these algebras are type III factors after restriction to coherent superselection sections and satisfy the duality condition. 
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     title = {Algebras of observables of the free {Dirac} field},
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}
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K. Yu. Dadashyan; S. S. Horuzhy. Algebras of observables of the free Dirac field. Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 2, pp. 166-182. http://geodesic.mathdoc.fr/item/TMF_1978_36_2_a2/

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